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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4600.3261', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.4666673232256737, -0.8844329309978143], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6548607339452851, 0.7557495743542583], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.5644432188667692, -0.825471896962774], 'algebraic': True, 'analytic_conductor': 21.362310190967847, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [23, [1]]], 'bad_primes': [2, 5, 23], 'central_character': '4600.3261', 'coeff_info': ['x^110 - 1', '0.998369103926136 + 0.0570888108627680*I', '\\\\zeta_{110}'], 'conductor': 4600, 'conductor_radical': 230, 'conjugate': 'dirichlet_L_4600.1941', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^91', 0, 0, 0, 'a^40', 0, 'a^72', 0, 'a^133', 0, 'a^147', 0, 0, 0, 'a^24', 0, 'a^119', 0, 'a^131', 0, 0, 0, 0, 0, 'a^163', 0, 'a^101', 0, 'a^74', 0, 'a^4', 0, 0, 0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.362310190967847, 'bad_primes': [2, 5, 23], 'central_character': '4600.3261', 'conductor': 4600, 'conductor_radical': 230, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4600/3261'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-4600-4600.3261-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-4600-4600.3261-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.362310190967847, 'root_angle': 0.3100354615430764, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25283155559', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4600.3261', 'Lhash_array': ['dirichlet_L_4600.3261'], 'factors': ['1-4600-4600.3261-r0-0-0'], 'label': '1-4600-4600.3261-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4600/3261'}